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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Class groups of complex quadratic fields


Author: R. J. Schoof
Journal: Math. Comp. 41 (1983), 295-302
MSC: Primary 12A25; Secondary 12-04, 12A50, 14K07
MathSciNet review: 701640
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Abstract: We present 75 new examples of complex quadratic fields that have 5-rank of their class groups $ \geqslant 3$. Only one of these fields has 5-rank of its class group $ > 3$: The field $ {\mathbf{Q}}(\sqrt { - 258559351511807} )$ has a class group isomorphic to

$\displaystyle C(5) \times C(5) \times C(5) \times C(5) \times C(2) \times C(11828).$

The fields were obtained by applying ideas of J. F. Mestre to the 5-isogeny $ {X_1}(11) \to {X_0}(11)$.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1983-0701640-0
PII: S 0025-5718(1983)0701640-0
Article copyright: © Copyright 1983 American Mathematical Society